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angle chasing, starting with right isosceles (2017 Kyiv City MO Round2 8.2)

Source:

September 10, 2020
anglesgeometryright triangleisosceles

Problem Statement

Triangle ABCABC is right-angled and isosceles with a right angle at the vertex CC. On rays CBCB on vertex BB is selected point F, on rays BABA on vertex AA is selected point G so that AG=BF.AG = BF. The ray GDGD is drawn so that it intersects with ray ACAC at point DD with ∠FGD=45o\angle FGD = 45^o. Find ∠FDG\angle FDG.
(Bogdan Rublev)
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